The Discovery of Color A Personal Perspective

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The Discovery of ColorA Personal Perspective

• O. W. Greenberg
• Miami 2007
• December 13, 2007

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Outline

• Developments in particle physics prior to the
  work on color.
• Discovery of color as a quantum number.
• Introduction of gauged SU(3) color.

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Particle physics prior to color

• The muon and pion had been discovered.
• Strange particles were found in cosmic rays.
• Lambda and Sigma hyperons.
• Kaon and antikaon, both charged and neutral.
• Xi, the cascade the Omega minus.
• Tau-theta puzzle.

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Accelerators come online

• About 1½ V events per day in a bubble chamber on
  a medium-height mountain.
• Separated beams of 106 Ks every 3 sec. at the
  AGS
• New problem to avoid swamping the detectors.
• Major problem at the LHC.

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Paradox copious production, slow decay.

• Attempt to understand using known dynamics
• Potential barriers, possibly connected with spin
  could inhibit decaysdid not work.

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Paradox copious production, slow decay,
(continued).

• A. Pais, associated production.
• Strangeness is conserved for rapid production by
  strong and electromagnetic interactions
• Violated for slow decay by weak interactions.

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Strangeness

• Gell-Mann, Nakano and Nishijimadisplaced charge
  multiplets.
• Nishijima, Gell-Mann formula, QI3Y/2.
• Weak interaction selection rules.

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K-zero, K-zero bar complex

• K1, K2 with different decay modes, lifetimes.
• Particle mixing effects, regeneration.
• Beautiful illustration of superposition principle
  of quantum theory.

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Tau-theta puzzle

• Tau?3 pi
• Theta?2 pi
• Same lifetimes
• Bruno Rossiprobably one particle

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Tau-theta puzzle, (continued)

• Dalitz analysis?different parities
• Parity was considered sacred
• The plot thickens
• The unexpected stimulates thought

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Tau-theta puzzle (continued)

• Suggestions by Lee and Yang
• Possible Interference Phenomena between Parity
  Doublets
• Question of Parity Conservation in Weak
  Interactions, 22 June 1956

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Tau-theta puzzle, (continued)

• Lee and Yang proposed parity doublets to explain
  this puzzle.
• Lee and Yang examined the data for conservation
  of parity, and found there was no evidence for
  parity conservation in weak interactions.
• Two solutions for one problemcant both be
  correct.

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Wigners comment

• Why should parity be violated before the rest of
  the Lorentz group?
• Why is that surprising?
• Discrete transformations are independent of the
  connected component of the Lorentz group.

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Parity violation was found earlier?

• Double scattering of beta decay electrons,
• R.T. Cox, et al., PNAS 14, 544 (1928).
• Redone with electrons from an electron gun with
  much higher statistics. No effect seen,
• C.J. Davisson and L.H. Germer,
• Phys. Rev. 33, 760 (1929).

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Wightman, Axiomatic Quantum Field Theory

• Asymptotic condition in quantum field
  theoryformalization of LSZ scattering theory.
• Purely theoreticalno numbers, except to label
  pages and equations.
• Operator-valued distributions, relative
  mathematical rigor.

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Divergent influences

• Very simple ideas used to classify newly
  discovered particles.
• Sophisticated techniques based on quantum field
  theory.

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Interest in identical particles

• Why only bosons or fermions?
• Are there other possibilities?
• H.S. Greens parastatistics (1953) as a
  generalization of each type.
• Bosonparaboson, order p,
• Fermionparafermion, order p
• p1 is Bose or Fermi.

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1962 Naples, Istanbul, SACLAY

• Axiomatic version of parastatistics with
  DellAntonio and Sudarshan in Naples.
• Presented at NATO summer school in Bebek, near
  Istanbul.
• Starting a collaboration with Messiah after
  giving a talk at SACLAY.

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Istanbul

• NATO summer school organized by Feza Gursey at
  the Robert College in Bebek
• Eduardo Caianiello, Sidney Coleman, David
  Fairlie, Shelly Glashow, Arthur Jaffe, Bruria
  Kauffman, Louis Michel, Giulio Racah, Eugene
  Wigner

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SACLAY with Messiah

• Albert Messiah, who fought with the Free French
  army of General Leclerc, was at SACLAY
• Entering SACLAY with guards on either side.

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Generalized statistics

• First quantized theory that allows all
  representations of the symmetric group.
• Theorems that show the generality of
  parastatisticsGreens ansatz is not necessary.

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1964

• Crucial year for the discovery of quarks and
  color.

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The crucial year, 1964

• Gell-Mannquarkscurrent quarks.
• Zweigacesconstituent quarks.
• Why only qqq and q-qbar?
• No reason in the original models.

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Background, Princeton, Fall 1964

• Relativistic SU(6), Gursey and Radicati
• Generalization of Wigners nonrelativistic
  nuclear physics idea to combine SU(2)I with
  SU(2)S to get an SU(4) to classify nuclear
  states.
• Gursey and Radicati combined SU(3)f with SU(2)S
  to get an SU(6) to classify particle states.

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SU(6) classifications
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Mesons
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Baryons
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Statistics paradox

• 56
• 70
• 20

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Attempts to make a higher dimensional
relativistic theory

• U(6,6)
• U(12)
• GL(12,C)
• Pais, Salam, et al, Freund, et al.
• Pais, Rev. Mod. Physics 38, 215 (1966).

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Magnetic moment ratio

• Beg, Lee, and Pais

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Previous calculations of magnetic moments

• Complicated calculations using pion clouds
  failed.
• Nobody even realized that the ratio was so simple.

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Significance of the magnetic moment calculation

• A simple one-line calculation gave the ratio
  accurate to 3.
• Very convincing additional argument for the quark
  model.
• Quarks have concrete reality.

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The spin-statistics theorem

• Particles that have integer spin
• must obey Bose statistics
• Particles that have odd-half-integer spin must
  obey Fermi statistics.

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Generalized spin-statistics theorem

• Not part of general knowledge
• Particles that have integer spin must obey
  parabose statistics and particles that have
  odd-half-integer spin must obey parafermi
  statistics.
• Each family is labeled by an integer p p1 is
  ordinary Bose or Fermi statistics.

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Parafermi quark model, 1964

• Suggested a model in which quarks carry order-3
  parafermi statistics.
• This allows up to three quarks in the same
  space-spin-flavor state without violating the
  Pauli principle, so the statistics paradox is
  resolved.
• This leads to a model for baryons that is now
  accepted.

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Resolution of the statistics paradox

• Exhilaratedresolving the statistics problem
  seemed of lasting value.
• Not interested in higher relativistic groups
  from ORaifeartaighs and my own work I knew that
  combining internal and spacetime symmetries is
  difficult or impossible..

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No-go theorems

• Later work of Coleman and Mandula and of Haag,
  Lopuszanski and Sohnius showed that the only way
  to combine internal and spacetime symmetries in a
  larger group is supersymmetry.

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Baryon spectroscopy

• Hidden parafermi (color) degree of freedom takes
  care of the required antisymmetry of the Pauli
  principle.
• Quarks can be treated as Bosons in the visible
  space, spin and flavor degrees of freedom.

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Table of excited baryons

• Developed a simple bound state model with s and p
  state quarks in the 56, L0 and 70, L1
  supermultiplets.

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Later developments of baryon spectroscopy

• OWG, Resnikoff
• Dalitz, and collaborators
• Isgur and Karl
• Riska and collaborators

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How did the physics community react?

• J. Robert Oppenheimer
• Steven Weinberg

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Gave Oppenheimer a preprint in Princeton

• Met him at a conference in Maryland
• Greenberg, its beautiful!

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Oppenheimers response, (continued)

• but I dont believe a word of it.

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Weinberg, The making of the standard model

• At that time I did not have any faith in the
  existence of quarks. (1967)

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Sources of skepticism

• Quarks had just been suggested.
• Fractional electric charges had never been seen.
• Gell-Mann himself was ambiguous.

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Gell-Manns comments

• It is fun to speculate if they were physical
  particles of finite mass (instead of purely
  mathematical entities as they would be in the
  limit of infinite mass).A search would help to
  reassure us of the non-existence of real quarks.

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Skepticism, continued

• Assuming a hidden degree of freedom on top of the
  fractionally charged unseen quarks seemed to
  stretch credibility to the breaking point.
• Some felt that parastatistics was inconsistent.

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Other solutions to the statistics paradox

• Explicit color SU(3), Han-Nambu, 1965
• Complicated antisymmetric ground state
• Quarks are not real anyway
• Other models

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Other solutions

• Explicit color SU(3)Han-Nambu, 1965
• Used three dissimilar triplets in order to have
  integer charges.
• Introduce now eight gauge vector fields which
  behave as (1,8), namely as an octet in SU(3)''.

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Color electromagnetism commute

• Identical fractional electric charges allow color
  electromagnetism to commute.
• Allows color to be an exact, unbroken, symmetry.
• Crucial part of understanding of quantum
  chromodynamics, QCD.

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Attempt to avoid a new degree of freedom

• Dalitz preferred a complicated ground state that
  would avoid the statistics problem.
• As rapporteur Dalitz always put a model with
  Fermi quarks first.
• The first rapporteur who preferred the
  parastatistics model was Harari, Vienna, 1968.

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Arguments for a simple ground state

• General theorems lead to an s-wave ground state.
• The simplest antisymmetric polynomial in the
  quark coordinates is

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Arguments for a simple ground state (continued)

• Then not clear what to choose for excited
  states.
• The polynomial
• vanishes because the coordinates are
  linearly dependent.
• Adding pairs leads to unseen exploding
  SU(3) states that are not seen.

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Arguments for a simple ground state (continued)

• Zeroes in the ground state wave function
  would lead to
• zeroes in the proton electric and magnetic form
  factors, which are not seen.

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If quarks are not real?

• If quarks are just mathematical constructs, then
  their statistics is irrelevant.

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Other models

• Baryonettes, in which 9 objects (baryonettes)
  compose a hadron.
• Many other models.

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Saturation

• Why are the hadrons made from just two
  combinations,

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Work with Zwanziger, 1966

• We surveyed existing models and constructed new
  models to account for saturation.
• The only models that worked were the parafermi
  model, order 3, and the equivalent three-triplet
  or color SU(3) models.

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Equivalence as a classification symmetry

• States that are bosons or fermions in the
  parafermi model, order 3,
• are in
• one-to-one correspondence with the states that
  are color singlets in the SU(3) color model.

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Relations and differences between the models
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Properties that require gauge theory

• Confinement
• S. Weinberg, 1973
• D.J. Gross and F. Wilczek, 1973
• H. Fritzsch, M. Gell-Mann and H. Leutwyler, 1973

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Properties that require gauge theory (continued)

• Asymptotic freedom,
  Gross, Wilczek, 1973
• Politzer, 1973
• Reconciles quasi-free quarks of the parton model
  with confined quarks of low-energy hadrons

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Properties that require gauge theory (continued)

• Running of coupling constants and precision tests
  of QCD.
• Jets in high-energy collisions.

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Summary of introduction of color

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Two facets of strong interaction

• Color as a classification symmetry and a global
  quantum number
• parafermi model (1964)
• was the first introduction of color as a global
  quantum number.
• SU(3) color as a local gauge theory
• Han-Nambu model (1965) was the first
  introduction of gauged SU(3) color.

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Outstanding puzzles of the standard model

• The reason for three generations of quarks and
  leptons,
• Origin of quark masses and the CKM matrix,
• Does the Higgs exist, if not what replaces it?

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Conclusion

• I reviewed the discovery of color, one of the
  properties of the standard model.
• Not clear where the next advances will come
  fromsimple physical ideas or deep mathematically
  motivated concepts. Time, and new experimental
  data, will tell.